Method and apparatus for measuring prospective short circuit current

ABSTRACT

A method of determining a prospective short circuit current for an electrical system including a source includes connecting a test load between either: (i) a first phase line and a second phase line of the electrical system or (ii) the first phase line and the neutral line of the electrical system, employing a sensor coupled to the electrical system to measure a voltage drop across the test load, determining a voltage value based on at least the measured voltage drop across the test load, determining a total effective impedance for the first phase line to the source, and determining the prospective short circuit current based on the voltage value and the total effective impedance.

BACKGROUND Field

The disclosed concept pertains generally to circuit protection devices,such as, without limitation, a circuit breaker, and, in particular, to amethod and apparatus for dynamically determining the prospectiveshort-circuit current of the circuit in which a circuit protectiondevice is provided.

Background Information

Circuit protection devices, such as circuit breakers, are well known inthe art. Circuit protection devices are used to protect the circuitry inan electrical system from damage due to an overcurrent condition, suchas an overload condition or a relatively high level short circuit orfault condition. Such circuit protection devices have a short circuitcurrent rating (SCCR), which identifies the maximum current the circuitprotection device is rated to safely interrupt. When a circuitprotection device is to be implemented in an electrical system, it isimportant to choose a circuit protection device that is properly ratedfor the system at the time of installation. The primary method forchoosing a properly rated circuit protection device is to firstdetermine what is known as the prospective short circuit (PSC) currentfor the electrical system, which is the highest electric current thatcan exist in the electrical system under short-circuit conditions, andthen choose a circuit protection device that has an SCCR that issufficient for the determined PSC current. In addition, the PSC currentin an electrical system can dynamically change over time based on thesource(s) present (e.g., PSC current may change due to a transfer from autility feed to an inverter based distributed energy source). In suchsituations, it may be necessary to dynamically alter the settings of acircuit protection device to handle different PSC current levels asneeded. It is therefore advantageous to be able to dynamically measurePSC current levels so that such adjustments can be made accordingly. PSCcurrent is also used to calculate arc flash incident energy values in anelectrical system, which values assist personnel by specifying arc flashhazards.

One known method for dynamically determining the PSC current in anelectrical system is described in U.S. Pat. No. 8,493,012, owned by theassigned hereof. That method utilizes an existing switch (contactor) andthe actual load in an electrical system in order to calculate the PSCcurrent based on voltage and current measurements made before and afterclosing the switch to energize the load. More specifically, in thatmethod, PSC current is calculated based on the resistance of the source,which results in a higher value of PSC current than the actual valuebased on total impedance (resistance+reactance). This is acceptable interms of safety because it over-specifies the breaker rating and arcflash incident energy, but results in extra cost.

There is thus room for improvement in the field of dynamic measurementof PSC current.

SUMMARY

In one embodiment, a method of determining a prospective short circuitcurrent for an electrical system including a source is provided. Themethod includes connecting a test load between either: (i) a first phaseline and a second phase line of the electrical system or (ii) the firstphase line and the neutral line of the electrical system, employing asensor coupled to the electrical system to measure a voltage drop acrossthe test load, determining a voltage value based on at least themeasured voltage drop across the test load, determining a totaleffective impedance for the first phase line to the source, anddetermining the prospective short circuit current based on the voltagevalue and the total effective impedance.

In another embodiment, an electrical device structured to be coupled toan electrical system between a source and a load and for determining aprospective short circuit current is provided. The electrical deviceincludes a test load, a switch structured to selectively connect thetest load between either: (i) a first phase line and a second phase lineof the electrical system or (ii) the first phase line and the neutralline of the electrical system, a sensor structured to generate a signalindicative of a voltage drop across the test load, and a controllerstructured and configured to determining a voltage value based on atleast the signal indicative of a voltage drop across the test load,determine a total effective impedance for the first phase line,determine a prospective short circuit current for the electrical systembased on the voltage value and the total effective impedance.

BRIEF DESCRIPTION OF THE DRAWINGS

A full understanding of the disclosed concept can be gained from thefollowing description of the preferred embodiments when read inconjunction with the accompanying drawings in which:

FIGS. 1A and 1B are schematic circuit diagrams of an electrical systemwhich illustrate a method of determining the PSC current according toone exemplary embodiment of the disclosed concept;

FIGS. 2A and 2B are schematic circuit diagrams of an electrical systemwhich illustrate a method of determining the PSC current according toanother, alternative exemplary embodiment of the disclosed concept;

FIG. 3 is a schematic diagram of an electrical system according to anexemplary embodiment that includes a circuit breaker that implements aline-to-line method of PSC current determination of the disclosedconcept;

FIG. 4 is a schematic diagram of an electronic trip unit that may beemployed to implement the disclosed concept; and

FIG. 5 is a schematic diagram of an electrical system according to analternative exemplary by that includes a circuit breaker that implementsa line-to-neutral method of PSC current determination of the disclosedconcept.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Directional phrases used herein, such as, for example, left, right,front, back, top, bottom and derivatives thereof, relate to theorientation of the elements shown in the drawings and are not limitingupon the claims unless expressly recited therein.

As used herein, the term “number” shall mean one or an integer greaterthan one (i.e., a plurality).

As used herein, the statement that two or more parts are “coupled”together shall mean that the parts are joined together either directlyor joined through one or more intermediate parts.

As used herein, the term “controller” shall mean a programmable analogand/or digital device (including an associated memory part or portion)that can store, retrieve, execute and process data (e.g., softwareroutines and/or information used by such routines), including, withoutlimitation, a field programmable gate array (FPGA), a complexprogrammable logic device (CPLD), a programmable system on a chip(PSOC), an application specific integrated circuit (ASIC), amicroprocessor, a microcontroller, a programmable logic controller, orany other suitable processing device or apparatus. The memory portioncan be any one or more of a variety of types of internal and/or externalstorage media such as, without limitation, RAM, ROM, EPROM(s),EEPROM(s), FLASH, and the like that provide a storage register, i.e., anon-transitory machine readable medium, for data and program codestorage such as in the fashion of an internal storage area of acomputer, and can be volatile memory or nonvolatile memory.

The disclosed concept provides two similar methods, namely aline-to-line method and a line-to-neutral method, that may be used todynamically measure the PSC current (I_(PSC)) in an electrical system.As described in detail herein, both methods determine the PSC currentbased on a voltage that is measured across a test load, such as a testresistor, and a calculated value of the impedance from the test point tothe source. The disclosed concept thus enables PSC currentdeterminations to be made directly within an electrical device such as,without limitation, a circuit breaker, a protective relay, or a meter,at any time.

I. The Line-to-Line Method

The line-to-line method will be described in connection with anexemplary electrical system 2 shown in FIG. 1A, which is redrawn in partin FIG. 1B. Referring to FIG. 1A and FIG. 1B, electrical system 2includes a three phase low voltage network 4 that is connected to athree phase load 6. Network 4 includes an AC source 10A (V_(R))connected to a phase line 12A, an AC source 10B (V_(S)) connected to aphase line 12B, and an AC source 10C (V_(T)) connected to a phase line12C. Each phase line 12A, 12B and 12C has an associated total effectiveimpedance for the phase, Z_(S), wherein Z_(S)=R_(S)+jX_(S). As seen inFIG. 1A and FIG. 1B, and according to an aspect of the disclosedconcept, a test resistor 14 (R_(L)) is connected between two phase lines(phase line 12A and phase line 12B in the illustrated example), such asthrough a mechanism like a solid state switch (not shown). As describedin detail elsewhere herein, in particular exemplary embodiments, testresistor 14 is connected between the two phase lines for a predeterminedperiod of time, such as, without limitation, a half cycle of theassociated source voltage. As will be appreciated, a loop current,I_(L), will flow line to line as shown (an arbitrary direction ofcurrent is shown in the FIG. 1A).

A. Empirical Solution

According to an empirical solution of the present embodiment of thedisclosed concept:

$\begin{matrix}{I_{L} = {\frac{V_{S} - V_{T}}{Z_{eq}} = \frac{V_{{Line} - {Line}}({nominal})}{{2Z_{s}} + Z_{L}}}} & (1)\end{matrix}$In the present empirical solution, Z_(L)=R_(L), and Z_(eq) is the totalequivalent impedance in the loop shown including test resistor 14 inFIG. 1B (i.e., Z_(eq) equals Z_(S) of the two phases in the loop andZ_(L) of test resistor 14). In addition, Z_(s) can be calculated fromthe above equation since the measured current I_(L) (=V_(drop)/R_(L)) isknown and Z_(L)=R_(L). The I_(PSC) (Line to Earth) is calculated asfollows:

$\begin{matrix}{{{I_{PSC}\left( {{Line} - {Earth}} \right)} = \frac{V_{Ph}}{Z_{s}}},} & (2)\end{matrix}$whereas, the I_(PSC) (Line to Line) is calculated as follows:

$\begin{matrix}{{I_{PSC}\left( {{Line} - {Line}} \right)} = {\frac{V_{Line}}{2Z_{s}} = {\frac{\sqrt{3}}{2}{\frac{V_{Ph}}{Z_{s}}.}}}} & (3)\end{matrix}$Equation (1) above is valid only if Z_(s) contains negligible reactance.However, in practical cases, there is some source reactance (e.g., thereactance of the secondary of a transformer), so use of equation (1)can, in practice, produce erroneous results.

In order to address this potential for erroneous results, providedbelow, according to a further aspect of the disclosed concept, is a morea precise solution for power factors of 0.7 and 0.9 wherein theneglected reactance is incorporated for additional precision.

B. Precise Solution—Power Factor 0.7

In the precise solution of the present embodiment of the disclosedconcept, instead of equation (1), I_(L) will follow the relation below(see FIG. 1B):

$\begin{matrix}{Z_{eq} = \sqrt{\left( {{2R_{s}} + R_{L}} \right)^{2} + \left( {2X_{s}} \right)^{2}}} & (4) \\{I_{L} = {\frac{V_{S} - V_{T}}{Z_{eq}} = {\frac{V_{{Line} - {Line}}}{\sqrt{\left( {{2R_{s}} + R_{L}} \right)^{2} + \left( {2X_{s}} \right)^{2}}}.}}} & (5)\end{matrix}$From the measured results:

$\begin{matrix}{Z_{eq} = {\frac{V_{Line}({nominal})}{I_{Loop}({measured})}.}} & (6)\end{matrix}$

Now, in equation (4), there are two unknown variables, R_(s) and X_(s).Z_(eq) can be calculated from relation (6) and R_(L) is known. In orderto reduce the number of unknown variables from two to one, thedistribution load power factor 0.7 is considered as follows: pf=cosϕ=cos(tan⁻¹(X/R)). If pf=0.7, from the above relation X/R=1, or X=R.Hence, putting R_(s)=X_(s) in equation (4), the following is obtained:8R_(s) ²+4R_(L)R_(s)+(R_(L) ²−Z_(eq) ²)=0. This is a simple quadraticequation, which is solved for positive values of R_(s), so that Z_(s)can be calculated from equation (7) below:Z _(s)=√{square root over ((R _(s) ² +X _(s) ²))}=√{square root over(2)}R _(s),  (7)and subsequently line to line I_(PSC) for the precise solution can becalculated from Equation (3) above.

C. Precise Solution—Power Factor 0.9

Alternatively, the distribution load power factor 0.9 is considered asfollows: If pf=0.9, X/R=0.48, or X=0.48R; Hence putting R_(s)=0.48X_(s)in equation (5), the following is obtained: 4.92R_(s)²+4R_(L)R_(s)+(R_(L) ²−Z_(eq) ²)=0. This is again a quadratic equation,which is solved for positive value of R_(s), so that Z_(s) can becalculated from the following relation and subsequently line to lineI_(PSC) from equation (3),Z _(s)=√{square root over (R _(s) ² =X _(s) ²)}=1.23R _(s)  (8)

Thus, in short, in the line-to-line method, I_(PSC) is determinedaccording to equation (3) based on V_(Line) and Z_(S). V_(Line) isdetermined by measuring the voltage across test resistor 14 that isprovided between two phases. Z_(S) (the total effective impedance forthe phase) is calculated for the circuit from a value of R_(S) (thetotal effective resistance for the phase) that is determined for thecircuit. R_(S) is calculated as described herein (by solving a simplequadratic equation) based on the known resistance, R_(L), of testresistor 14, and a value of Z_(eq) (the total equivalent impedance inthe loop) that is calculated as described herein based on the knownnominal line voltage and the measured loop current for the circuit.

II. The Line-to-Neutral Method

The line-to-neutral method will be described in connection with anexemplary electrical system 16 shown in FIG. 2A, which is redrawn inpart in FIG. 2B. Referring to FIG. 2A and FIG. 2B, electrical system 16includes a three phase low voltage network 18 that is connected to athree phase load 20. Network 18 includes an AC source 22A (V_(R))connected to a phase line 24A, an AC source 22B (V_(S)) connected to aphase line 24B, and an AC source 22C (V_(T)) connected to a phase line24C. Each phase line 24A, 24B and 24C has an associated total effectiveimpedance for the phase, Z_(S), wherein Z_(S)=R_(S)+jX_(S). As seen inFIG. 2A and FIG. 2B, and according to an aspect of the disclosedconcept, a test resistor 26 (R_(L)) is connected between a phase line(phase line 22C in the illustrated example) and a neutral line 28, suchas through a mechanism like a solid state switch (not shown). Asdescribed in detail elsewhere herein, in particular exemplaryembodiments, test resistor 26 is connected between the phase and neutrallines for a predetermined period of time, such as, without limitation, ahalf cycle of the associated source voltage. As will be appreciated, aloop current, I_(L), will flow line to neutral as shown (an arbitrarydirection of current is shown in the FIG. 2A).

A. Empirical Solution

According to an empirical solution of the present embodiment of thedisclosed concept:

$\begin{matrix}{I_{L} = {\frac{V_{S}}{Z_{eq}} = {\frac{V_{Ph}}{Z_{s} + Z_{L}} = \frac{V_{Ph}}{Z_{s} + R_{L}}}}} & (9)\end{matrix}$In the present empirical solution, Z_(L)=R_(L), and Z_(eq) is the totalequivalent impedance in the loop shown including test resistor 14 inFIG. 2B (i.e., Z_(eq) equal Z_(S) of the phase in the loop and Z_(L) oftest resistor 14). Z_(s) in this case (line to neutral loop) is the sumof impedance of the phase wire (24C) and the neutral wire (28). It canbe calculated from the above equation as the measured current I_(L) isknown and Z_(L)=R_(L). I_(PSC) is calculated as follows:

$\begin{matrix}{I_{PSC} = \frac{V_{Ph}}{Zs}} & (10)\end{matrix}$Solving equation (9) for Z_(s), the following is obtained:

$Z_{s} = {\frac{V_{Ph} - {I_{L}R_{L}}}{I_{L}} = \frac{V_{Ph} - V_{L}}{I_{L}}}$Putting this value of Z_(s) in equation (10), the following is obtained:

$I_{PSC} = {\frac{V_{Ph}}{\frac{V_{Ph} - V_{L}}{I_{L}}} = {\frac{I_{L}}{\frac{V_{Ph} - V_{L}}{V_{Ph}}} = \frac{I_{L}}{\% V_{drop}}}}$

However, equation (9) is valid only if Z_(S) contains negligiblereactance. In practical cases, there is some source reactance (e.g., thereactance of the secondary of a transformer), so equation (9) canproduce erroneous results. In order to address this potential forerroneous results, provided below, according to a further aspect of thedisclosed concept, is a more a precise solution for power factors of 0.7and 0.9 wherein the neglected reactance is incorporated for additionalprecision.

B. Precise Solution—Power Factor 0.7

In the precise solution of the present embodiment of the disclosedconcept, instead of equation (9), I_(L) will follow the followingrelation:

$\begin{matrix}{Z_{eq} = \sqrt{\left( {R_{s} + R_{L}} \right)^{2} + \left( X_{s} \right)^{2}}} & (11) \\{I_{L} = {\frac{V_{T}}{Z_{eq}} = \frac{V_{Ph}}{\sqrt{\left( {R_{s} + R_{L}} \right)^{2} + \left( X_{s} \right)^{2}}}}} & (12)\end{matrix}$From the measured results:

$\begin{matrix}{Z_{eq} = \frac{V_{Phase}({nominal})}{I_{Loop}({measured})}} & (13)\end{matrix}$Now, in equation (11), there are two unknown variables, R_(s) and X_(s).Z_(eq) can be calculated from relation (13) and R_(L) is already known.In order to reduce the unknown variables from two to one, thedistribution load power factor 0.7 is considered as follows: pf=cosϕ=cos(tan⁻¹(X/R)). If pf=0.7, X/R=1, or X=R. Hence, putting R_(s)=X_(s)in equation (11), the following is obtained: 2R_(s) ²+2R_(L)R_(s)+(R_(L)²−Z_(eq) ²)=0. This is a simple quadratic equation, which is solved forpositive value of R_(s), so that Z_(s) can be calculated from thefollowing relation (14) and Ipso from equation (10):Z _(s)=√{square root over (R _(s) ² +X _(s) ²)}=√{square root over (2)}R_(s).  (14)

C. Precise Solution—Power Factor 0.9

Alternatively, the distribution load power factor 0.9 is considered asfollows: if pf=0.9, X/R=0.48, or X=0.48R. Hence, putting R_(s)=0.48X_(s)in equation (11), the following is obtained: 1.23R_(s)²+2R_(L)R_(s)+(R_(L) ²−Z_(eq) ²)=0. This is again a quadratic equation,which is solved for positive value of R_(s), so that Z_(s) can becalculated from the following relation (15) and I_(PSC) from equation(10):Z _(s)=√{square root over (R _(s) ² +X _(s) ²)}=√{square root over(1.23)}R _(s).  (15)

Thus, in short, in the line-to-neutral method, I_(PSC) is determinedaccording to equation (10) based on V_(Ph) and Z_(S). V_(Ph) isdetermined by measuring the voltage across test resistor 14 that isprovided between a phase line and the neutral line. Z_(S) (the totaleffective impedance for the phase) is calculated for the circuit from avalue of R_(S) (the total effective resistance for the phase) that isdetermined for the circuit. R_(S) is calculated as described herein (bysolving a simple quadratic equation) based on the known resistance,R_(L), of test resistor 14, and a value of Z_(eq) (the total equivalentimpedance in the loop) that is calculated as described herein based onthe known nominal phase voltage and the measured loop current for thecircuit.

As described above, in the exemplary embodiment, in both theline-to-line method and the line-to-neutral method, the test load (e.g.,test resistor 14 or 26) is connected through a solid state switch. Thevoltage drop across the solid state switch is not considered in theabove calculations. However, for increased precision, the impedance ofthe solid state switch should be excluded from the total calculatedimpedance Z_(S). Specifically, in one particular embodiment, theimpedance of the solid state switch is determined and that value issubtracted from the calculated Z_(S) (see above) to create a modifiedZ_(S) (i.e., Z_(S)−Z_(switch)). The modified Z_(S) is then used tocalculate I_(PSC) as described herein.

There are various ways to determine the impedance of the solid stateswitch. In the exemplary embodiment, the solid state switch is made upof two thyristors. The voltage drop across the thyristors (V_(T)) isdetermined from the corresponding value of the loop current I_(L)=I_(T)(=voltage drop across loop resistor/loop resistor value in ohms). Then,the impedance of the solid state switch is determined from the followingrelation:

$\begin{matrix}{Z_{switch} = \frac{V_{T}}{I_{T}}} & (16)\end{matrix}$Since the curve of the forward characteristic of the thyristors is knownto be non-linear, the switch impedance is not constant and needs to bedetermined for each loop current value.

III. Exemplary Implementations

FIG. 3 is a schematic diagram of an electrical system 30 according toone particular, non-limiting exemplary embodiment of the disclosedconcept. As seen in FIG. 3, electrical system 30 includes a 3-phase ACsupply 32, a 3-phase load 34, and a circuit breaker 36 provided between3-phase AC supply 32 and 3-phase load 34. As described in detail below,circuit breaker 36 is structured and configured to provide overcurrentprotection to 3-phase load 34. In addition, as also described in detailbelow, circuit breaker 36 is further structured and configured toimplement the line-to-line method of determining PSC current of thedisclosed concept that is described in detail elsewhere herein.

Referring to FIG. 3, circuit breaker 36 includes separable contacts 38A,38B, and 38C, operating mechanisms 42A, 42B, and 42C, an electronic tripunit 44, and current sensors 46A, 46B and 46C. As seen in FIG. 3,separable contacts 38A are provided in a first phase line 40A ofelectrical system 30, separable contacts 38B are provided in a secondphase line 40B of electrical system 30, and separable contacts 38C areprovided in a third phase line 40C of electrical system 30. Eachoperating mechanism 42A, 42B, 42C is structured to, under the control ofelectronic trip unit 44, open and close the associated separablecontacts 38A, 38B, 38C. More specifically, electronic trip unit 44 isstructured and configured to control each of the operating mechanisms42A, 42B, 42C to trip open the associated separable contact 38A, 38B,38C when, as described below, conditions dictate that such opening isnecessary based on the outputs of current sensors 46A, 46B and 46C.

FIG. 4 is a schematic diagram showing certain selected components ofelectronic trip unit 44 according to the exemplary embodiment. As seenin FIG. 4, electronic trip unit 44 includes a controller 58 comprising amicroprocessor (μP) 60 and a memory portion including a random accessmemory (RAM) 62 and an EEPROM 64. Electronic trip unit 44 furtherincludes an analog-to-digital converter (ADC) 66 that is structured toreceive the output signals from current sensors 46A, 46B and 46C andconvert those signals to digital data that is appropriate formicroprocessor 60. RAM 62 stores a trip unit program that is executableby microprocessor 60. The trip unit program includes a number ofroutines that are configured to determine whether and when to issue atrip signal for tripping each of the operating mechanisms 42A, 42B, 42Cbased upon the current sensed by each of the current sensors 46A, 46B,46C. In addition, EEPROM 64 stores (in nonvolatile memory) thefunctional trip settings of electronic trip unit 44 which define theoperating characteristics thereof, and which are read intomicroprocessor 60 as needed by the trip unit program.

In addition, referring again to FIG. 3, circuit breaker 36 furtherincludes additional circuitry for implementing the line-to-line methodfor determining I_(PSC) of the disclosed concept. In particular, circuitbreaker 36 includes a loop circuit 48 that is provided between the phaseline 40A and the phase line 40B in the illustrated example. Loop circuit48 includes a solid state switch 50, a test resistor 52, a voltagesensor 54 coupled to measure the voltage drop across the test resistor52, and a current sensor 56 coupled to measure the loop current flowingthrough loop circuit 48. Solid state switch 50 is connected to and iscontrolled by (i.e., opened and closed by) electronic trip unit 44. Inaddition, both voltage sensor 54 and current sensor 56 are connected toelectronic trip unit 44 (through ADC 66) such that the output signalsthereof are provided to electronic trip unit 44. Note that, while onlyone loop circuit 48 is shown in FIG. 3 for ease of illustration, it willbe understood that additional loop circuits 48 provided between thephase line 46A and phase line 46C and/or in between phase line 46B andphase line 46C for making I_(PSC) measurements based thereon may also beincluded within the scope of the disclosed concept.

Furthermore, according to an aspect of the exemplary embodiment, RAM 62stores a number of routines which are executable by microprocessor 60which implement the line-to-line method of the disclosed concept fordetermining PSC current using the circuitry of loop circuit 48 describedabove. In particular, the routines are structured and configured tocontrol circuit breaker 36 to operate as follows. When PSC current is tobe measured, electronic trip unit 44 will issue a switch control signal(FIG. 4) which causes solid state switch 50 to be closed for apredetermined number of periods (e.g., multiple periods), with eachperiod being of a predetermined duration. In the non-limiting, exemplaryembodiment, each period is a positive (or negative) half cycle of theapplied AC voltage. For each period during which solid state switch 50is closed, the following parameters are determined/measured: (i) thenominal line-to-line voltage for loop circuit 48 (e.g., measuredcontinuously in electronic trip unit 44), (ii) the loop current, I_(L),through loop circuit 48, and (iii) the voltage drop, V_(LINE), acrossloop resistor 52 of loop circuit 48. Then, each of those measured valuesduring multiple periods is averaged to provide an average nominalline-to-line voltage, an average V_(LINE), and an average I_(L). Next,Z_(S) is calculated as described herein using the average nominalline-to-line voltage and the average I_(L). Finally, I_(PSC) iscalculated as described herein using the average V_(LINE) and thecalculated Z_(S).

It will be appreciated that the exemplary embodiment just described thatemploys average values for nominal line-to-line voltage, I_(L) andV_(LINE) is meant to be exemplary only, and that single measurements ofthose values as opposed to averages may also be employed within thescope of the disclosed concept. Furthermore, while the exemplaryembodiment makes measurements over multiple positive half cycle of theapplied AC voltage, it will also be understood that that is meant to beexemplary only and that measurements may also be made over negative halfcycles instead of or in addition to the positive half cycles. In fact,an implementation that uses both positive and opposite, negative halfcycles may account for differences (i.e., imbalances) in the sourceimpedance, and therefore may be advantageous.

FIG. 5 is a schematic diagram of an electrical system 30′ according toan alternative particular, non-limiting exemplary embodiment of thedisclosed concept. Electrical system 30′ is similar to electrical system30 described above, and like components are labeled with like referencenumerals. However, electrical system 30′ is structured and configured toimplement the line-to-neutral method of determining PSC current of thedisclosed concept that is described in detail elsewhere herein.

In particular, electrical system 30′ includes an alternative circuitbreaker 36′ that is similar to circuit breaker 36, except that itincludes a loop circuit 48′ that is provided between phase line 40A andthe neutral line. In this alternative embodiment, RAM 62 stores a numberof routines which are executable by microprocessor 60 which implementthe line-to-neutral method of the disclosed concept for determining PSCcurrent using the circuitry of loop circuit 48′. In particular, theroutines are structured and configured to control circuit breaker 36′ tooperate as follows. When PSC current is to be measured, electronic tripunit 44 will issue a switch control signal (FIG. 4) which causes solidstate switch 50 to be closed for a predetermined number of periods(e.g., multiple periods), with each period being of a predeterminedduration. In the non-limiting, exemplary embodiment, each period is apositive half cycle of the applied AC voltage. For each period duringwhich solid state switch 50 is closed, the following parameters aredetermined/measured: (i) the nominal phase voltage for loop circuit 48′(e.g., measured continuously in electronic trip unit 44), (ii) the loopcurrent, I_(L), through loop circuit 48′, and (iii) the voltage drop,V_(Ph), across loop resistor 52 of loop circuit 48′. Then, each of thosemeasured values is averaged to provide an average nominal phase voltage,an average V_(Ph), and an average I_(L). Next, Z_(S) is calculated asdescribed herein using the average nominal phase voltage and the averageI_(L). Finally, I_(PSC) is calculated as described herein using theaverage V_(Ph) and the calculated Z_(S).

As was the case with electrical system 30 described above, it will beappreciated that the exemplary embodiment just described that employsaverage values for nominal phase voltage, I_(L) and V_(Ph) is meant tobe exemplary only, and that single measurements of those values asopposed to averages may also be employed within the scope of thedisclosed concept. Furthermore, while the exemplary embodiment makesmeasurements over multiple positive half cycle of the applied ACvoltage, it will also be understood that that is meant to be exemplaryonly and that measurements may also be made over negative half cycleinstead of or in addition to the positive half cycles.

In addition, in further alternative embodiments, electronic trip unit 44in either circuit breaker 36 or circuit breaker 36′ is furtherstructured and configured to adjust the functional trip settings storedin EEPROM 64 and used by the trip program of electronic trip unit 44based on the determined I_(PSC).

Moreover, in still a further embodiment, circuit breaker 36 and circuitbreaker 36′ may be combined to form a device that implements both theline-to-line method and the line-to-neutral method of the disclosedconcept by including loop circuits 48 and 48′ described herein in asingle device.

It will be understood that circuit breakers 36 and 36′ are describedherein in order to provide exemplary implementations of an electricaldevice in which the disclosed concept may be implemented. It will beunderstood, however, that that is meant to be exemplary only and thatthe methods of the disclosed concept may alternatively be integratedinto electrical devices other than circuit breakers, such as, withoutlimitation, protective relays or metering devices.

While specific embodiments of the disclosed concept have been describedin detail, it will be appreciated by those skilled in the art thatvarious modifications and alternatives to those details could bedeveloped in light of the overall teachings of the disclosure.Accordingly, the particular arrangements disclosed are meant to beillustrative only and not limiting as to the scope of the disclosedconcept which is to be given the full breadth of the claims appended andany and all equivalents thereof.

What is claimed is:
 1. A method of determining a prospective shortcircuit current for an electrical system including a source and based ona power factor of either 0.7 or 0.9, comprising connecting a test loadbetween either: (i) a first phase line and a second phase line of theelectrical system or (ii) the first phase line and a neutral line of theelectrical system; employing a sensor coupled to the electrical systemto measure a voltage drop across the test load; determining a voltagevalue based on at least the measured voltage drop across the test load;determining a total effective impedance (Z_(s)) for the first phase lineto the source, wherein Z_(s) is equal to Z_(S)=R_(S)±jX_(S), whereinR_(s) is a total resistance for the first phase line to the source andX_(s) is a total reactance for the first phase line to the source,wherein Z_(s) is calculated from a positive value for R_(s) that isdetermined by solving a quadratic equation for R_(s), and wherein thequadratic equation is selected from the following quadratic equations:8R _(s) ²+4R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0,4.92R _(s) ²+4R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0,2R _(s) ²+2R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0, and1.23R _(s) ²+2R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0, wherein R_(L) is aresistance of the test load and wherein Z_(eq) is an equivalentimpedance value that is calculated based on either (i) a nominalline-to-line voltage for the electrical system and a current flowingthrough the test load, or (ii) a nominal phase voltage for theelectrical system and the current flowing through the test load; anddetermining the prospective short circuit current based on the voltagevalue and the total effective impedance.
 2. The method according toclaim 1, wherein the connecting comprises connecting the test loadbetween the first phase line and the second phase line by closing aswitch provided between the first phase line and the second phase line,and wherein the quadratic equation is selected from:8R _(s) ²+4R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0, and4.92R _(s) ²+4R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0.
 3. The methodaccording to claim 2, further comprising employing a current sensorcoupled to the electrical system to determine the current flowingthrough the test load when the test load is connected between the firstphase line and the second phase line.
 4. The method according to claim1, wherein the connecting comprises connecting the test load between thefirst phase line and the neutral line by closing a switch providedbetween the first phase line and the neutral line, and wherein thequadratic equation is selected from:2R _(s) ²+2R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0, and1.23R _(s) ²+2R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0.
 5. The methodaccording to claim 4, further comprising employing a current sensorcoupled to the electrical system to determine the current flowingthrough the test load when the test load is connected between the firstphase line and the neutral line.
 6. The method according to claim 1,wherein the test load is a test resistor.
 7. The method according toclaim 1, wherein the connecting the test load, the employing the sensor,the determining the voltage value, the determining the total effectiveimpedance, and the determining the prospective short-circuit current areall performed within a circuit protection device coupled to theelectrical system between the source and a load.
 8. The method accordingto claim 7, wherein the circuit protection device is a circuit breaker.9. An electrical device structured to be coupled to an electrical systembetween a source and a load and structured and configured to determine aprospective short circuit current for the electrical system based on apower factor of either 0.7 or 0.9, comprising: a test load; a switchstructured to selectively connect the test load between either: (i) afirst phase line and a second phase line of the electrical system or(ii) the first phase line and the neutral line of the electrical system;a sensor structured to generate a signal indicative of a voltage dropacross the test load; and a controller structured and configured to:determine a voltage value based on at least the signal indicative of avoltage drop across the test load, determine a total effective impedance(Z_(s)) for the first phase line, wherein Z_(s) is equal toZ_(S)=R_(S)+jX_(S), wherein R_(s) is a total resistance for the firstphase line to the source and X_(s) is a total reactance for the firstphase line to the source, wherein Z_(s) is calculated from a positivevalue for R_(s) that is determined by solving a quadratic equation forR_(s), and wherein the quadratic equation is selected from the followingquadratic equations:8R _(s) ²+4R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0,4.92R _(s) ²+4R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0,2R _(s) ²+2R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0, and1.23R _(s) ²+2R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0, wherein R_(L) is aresistance of the test load and wherein Z_(eq) is an equivalentimpedance value that is calculated based on either (i) a nominalline-to-line voltage for the electrical system and a current flowingthrough the test load, or (ii) a nominal phase voltage for theelectrical system and the current flowing through the test loaddetermine the prospective short circuit current for the electricalsystem based on the voltage value and the total effective impedance. 10.The electrical device according to claim 9, wherein the electricaldevice is a circuit protection device.
 11. The electrical deviceaccording to claim 10, wherein the electrical device is a circuitbreaker.
 12. The electrical device according to claim 9, wherein theswitch is structured to selectively connect the test load between thefirst phase line and the second phase line, the electrical devicefurther comprising a current sensor structured to determine the currentflowing through the test load when the test load is connected betweenthe first phase line and the second phase line, and wherein thequadratic equation is selected from:8R _(s) ²+4R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0, and4.92R _(s) ²+4R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0.
 13. The electricaldevice according to claim 9, wherein the switch is structured toselectively connect the test load between the first phase line and theneutral line, the electrical device further comprising a current sensorstructured to determine the current flowing through the test load whenthe test load is connected between the first phase line and the neutralline, and wherein the quadratic equation is selected from:2R _(s) ²+2R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0,and1.23R _(s) ²+2R _(L) R _(s)+(R _(L) ² −Z _(eq) ²)=0.
 14. The electricaldevice according to claim 9, wherein the test load is a test resistor.15. The electrical device according to claim 9, wherein the controlleris structured to adjust an operational parameter of the electricaldevice based on the determined prospective short circuit current. 16.The electrical device according to claim 15, wherein the electricaldevice is a circuit breaker and wherein the controller is structured toadjust functional trip settings of the circuit breaker based on thedetermined prospective short circuit current.